## Physics Questions People Ask Fermilab

What is a MeV in grams?

What is a MeV in grams? In the unlikely event that I fuse a couple of hydrogen nucleii what is the weight lost by the system? My reference says it's 3.2 MeV but that's not helpful.

Hi,

Let us start with eV (electron-volt). It is an energy unit used in High-energy physics. A MeV is the Mega electron-volt, e.g. million times more than eV. One eV is defined as the energy, that an electron ( or an other single-charged(q=1.6*10^-19 Coulombs) particle) gains when it undergoes a potential difference of 1 Volt. In the International units ( SI units) 1eV corresponds to 1.6*10^-19 Joules.

According to Einstein's formula E=mc^2, energy is equivalent to mass (and vice versa), up to the c^2 constant. In SI units, mass is in kilograms , and the speed of light is 3*10^8 m/s.

Therefore, 1eV energy corresponds to

m=(1.6*10^-19 Joules)/(9*10^16 m/s)= 1.8*10^-36 Kg=1.8*10^-33 grams.

Then 3.2 MeV corresponds to 3.2*10^6*1.8*10^-33 grams=5.7*10^-27 grams. Just as an illustration , the 3.2 MeV mass is roughly 6 times more than the rest mass of an electron.

While we're at it can you give me E =mc^2 in meaningful units, with the proportionality constant?

Chuck Walbridge

Well, what is a meaningful unit? For me it is the units of the SI system, mass in kilograms, length in meters, current in amperes, time in seconds, ... .

Then energy in Joules = 9*10^16*mass in kilograms.

If you give me your favorite energy units, we can rewrite this equation by finding the right proportionality constant.

Bye Arnold

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